Npower walked away from domestic energy supply and were bought out by E.ON due to no profit to be made in the UK serving households.
SSE became part of OVO two years ago due to the same reasons.
You focus on British Gas' profits, but actually, their retail arm has made losses despite their parent company, Centrica, making high profits. The reason for this is that businesses are subsidising domestic rates here, because the price cap has meant they are unprofitable which led to the downfall of npower and SSE in recent years.
In 2017, Centrica made £816 million in total operating profit. However, British Gas which sells to the household, made a loss of £71.9 million. And this hasn't really changed because of the wholesale price increases being even more massive and the price cap still being in place. This is precisely why the smaller firms, that are basically just trading desks because of reduced regulation on who can supply energy, went under en masse this past winter. A lot were undercapitalised and didn't hedge enough given how record high prices came about even before Ukraine entered the news. The other part of it is, there just isn't any money in selling to households compared to businesses and the international market.
You might also want to consider what those profits are to be used for. Sure, the gov't could make it so that Centrica et al basically sell you energy at cost or any profits go straight back to the taxpayers. What, then, do you do about our incredibly antiquated and perilously close to zero excess capacity infrastructure? Do we just not invest in it any more?
Do you want your children to have a future where it isn't 4 hours of 'leccy a day and gas limited to heavy industry only in the week? If no, then they need to be invested in.